In recent years, much research and development has been carried out in the field of image engineering into a technology for restoring an original image from a degraded image. That is to say, removing unnecessary information (blurring and noise) from a degraded image (received information) in which unnecessary information (blurring and noise) is mixed in with an original image (desired information, clear image), and extracting only the original image (desired information), is an essential technology in the field of image engineering, and has been the subject of much research and development in recent years. For example, an image captured by means of a digital camera (a generic term for a digital still camera and digital video camera), a mobile phone, or the like, inevitably shows image degradation in comparison with an original object due to the influence of “blurring” caused by camera shake, inaccurate focusing, or the like, and Gaussian or impulse “noise” caused by a dark current, thermal noise, or the like. “Image restoration” is the restoration of an image that is as close as possible to an original image from such a degraded image.
The majority of popular image restoration technologies currently on the market are preventive technologies that reduce the influence of blurring and noise in advance using, for example, camera shake correction, face recognition, color correction, various filters, and the like. As a result, in the field of digital cameras in particular, it has recently become possible to obtain vivid images easily through improved digital camera functionality and performance.
However, although there is no problem with such preventive technologies in circumstances in which images are recaptured numerous times, restoration for images that do not permit recapturing, as in the case of an already degraded image of an old document or the like, or images that change instantaneously in such fields as sport and medicine, remains a difficult problem. Here, images that change instantaneously in the fields of sport and medicine include, for example, an instantaneous action of a player, and instantaneous states of organs such as the heart and lungs. Therefore, image restoration in circumstances that do not permit recapturing has now become particularly important.
One widely known conventional image restoration technology for circumstances that do not permit recapturing is an image restoring method that uses a Wiener Filter (Non-Patent Literature 1, Non-Patent Literature 2). This method uses a filter that minimizes a mean squared error between a restored image obtained via a filter and an original image, and this filter is also called a least-squares filter. This method is an image restoring method in which processing is performed in the frequency domain, and therefore presupposes stationarity of a stochastic process and an image size of semi-infinite length.
Another known image restoration technology is an image restoring method that uses a projection filter (Non-Patent Literature 3, Non-Patent Literature 4). A projection filter evaluates closeness between an original image and a restored image, and minimizes a mean squared error of a restored image noise component among items for which an image component of noise of an original image has best approximation to individual original images—that is orthogonal projections of individual original images. From this property, a projection filter is a method of restoring a best-approximation image irrespective of frequency of appearance.
Yet another known image restoration technology is an image restoring method that uses a Kalman Filter (Non-Patent Literature 5, Non-Patent Literature 6). In this method, first, in step 1, an AR (Auto Regressive) system parameter (hereinafter referred to as “AR coefficient”) is estimated, and then, in step 2, a state space model (comprising a state equation and observation equation) is configured using the AR coefficient estimated in step 1, and high-performance image restoration is implemented by applying this Kalman filter theory (Kalman filter algorithm).